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Signals and Systems Concept Inventory Assessment Instruments
 

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Goal

The goal is to develop assessment instruments to measure change in the conceptual understanding of signals and systems by students from the beginning and to the end of an introductory signals and systems course that is typically offered late in the sophomore year or early in the junior year. Two separate versions of the Signals and Systems Concept Inventory (SSCI) have been developed for continuous time (CT SSCI) and discrete time (DT SSCI).

Both versions of the SSCI have been motivated by the Force Concept Inventory created by Halloun and Hestenes [14] and its impact on physics education. The Force Concept Inventory (FCI) was designed to measure conceptual, not computational, understanding of Newtonian Mechanics. The questions are posed to focus on intuitive comprehension independent of knowledge of the terminology or numerical modeling. Following the lead of the FCI, faculty members are creating concept inventories for other disciplines. More information about concept inventories can be found in a paper by Evans and Hestenes.[5]

For more information or to obtain a copy of either version of the SSCI, please contact , Electrical Engineering Department, George Mason University (GMU), or , Electrical Engineering Department, University of Massachusetts Dartmouth (UMD).

CT SSCI: Core Concepts

Version 2.0 of the CT SSCI contains 25 questions. The list below shows the core concepts covered by CT SSCI version 2.0. The numbers in parentheses next to each of the five main topics indicate how many questions in the current version of the exam address that topic. Note that the numbers do not add to 25 because questions covering more than one concept are counted multiple times.

  • Background mathematical concepts (6)
    • Basic signals, e.g., sinusoids and unit step functions
    • Basic signal manipulations, e.g., amplitude scaling, time shifting, time reversal
    • Forms of the solutions to linear, constant-coefficient differential equations
  • Linearity and time invariance (3)
  • Convolution (4)
    • Mechanics
    • Commutative and distributive properties
    • Relationship of impulse response and causality
  • Fourier and Laplace transform representations (15)
    • Fourier series
    • Connection between time and frequency domain properties of a signal
    • Fourier transform properties and theorems including linearity, conjugate symmetry, delay theorem, and modulation theorem
    • Effect of the poles and zeros of a system function on the frequency response, impulse response, and stability of causal systems
  • Filtering with LTI systems (2)
    • Infinite-extent sinusoids
    • Narrowband pulses
CT SSCI: Development Process

We began developing the continuous-time version of the SSCI in late 2000, and produced an initial draft in January of 2001. Version 1.0 of the CT SSCI consisted of 30 multiple-choice questions on the core concepts. In spring 2001 we administered the exam to 128 students at George Mason University and the University of Massachusetts Dartmouth. The test population consisted of undergraduate and graduate students from six courses in the areas of linear systems, signal processing, and communications. We had two primary goals for the alpha-testing phase: to examine the clarity and appropriateness of the questions and to investigate which alternate (distractor) answers were most attractive to the students.

For each question we asked students to select one of five prescribed choices or to fill in a response of their own, allowing us to capture novel incorrect answers caused by unanticipated confusions. The initial round of testing indicated that, while the questions were generally clear[1], the exam was too long and too difficult. Most students struggled to finish within the one-hour proposed time limit, and the mean score was 29.5/100. The difficulty of the exam is further illustrated by the fact that 87% of students scored below 40/100. Regarding the distractor analysis, Version 1.0 appeared to capture almost all common misconceptions since few students gave a solution different from the prescribed alternatives.

Based on the alpha-test results, we revised the CT SSCI during the summer of 2001 and made several important changes. First, we added several new questions that address the mathematical background knowledge required for the study of signals and systems. Second, we used the results of the distractor analysis to eliminate the least common alternate answers, resulting in four choices for each question. Finally, we reduced the total number of questions to 25 by focusing the exam on the most basic concepts.

DT SSCI: Status

The DT SCCI is in the alpha-testing phase. At present, students are using an answer sheet that helps the developers identify misconceptions on the part of students so that the developers can construct distractors (incorrect
answers that are related to commonly held misconceptions). For example, in the alpha version students can write in an alternate response to help identify possible distractors. The initial version of the DT SSCI has been given at the UMD and will be given at GMU. Post-exam interviews are being planned for GMU.

Web Resources

Signals and Systems Concept Inventory John R. Buck (University of Massachusetts Dartmouth) and Kathleen E. Wage (George Mason University) maintain a page with current information about both the continuous-time signals and systems concept inventory (CT-SSCI) and the discrete-time signals and systems concept inventory (DT-SSCI). From this page, faculty members can request access to current copies of both instruments.

References for further information

  1. Hestenes, David, Malcolm Wells, and Gregg Swackhamer, 1992. Force Concept Inventory. The Physics Teacher, 30 (3), 141151.
  2. Hestenes, David, and Ibrahim Halloun, 1995. Interpreting the Force Concept Inventory. The Physics Teacher, 33 (8).
  3. Halloun, Ibrahim, and David Hestenes, 1985. The initial knowledge state of college physics students. American Journal of Physics, 53(11), 10431055.
  4. Halloun, Ibrahim, and Hestenes, David, 1985. Common sense concepts about motion. American Journal of Physics, 53(11), 10561065.
  5. Evans, D.L., and Hestenes, David, 2001. "The Concept of the Concept Inventory Assessment Instrument," Proceedings, 2001 Frontiers in Education Conference, Reno, Nevada, 1013 October 2001.
  6. Wage, Kathleen E., and Buck, John R., 2001. "Development of the Signals and Systems Concept Inventory (SSCI) Assessment Instrument," Proceedings, 2001 Frontiers in Education Conference, Reno, Nevada, 1013 October 2001.
  7. Wage, K.E., Buck, J.R., Welch, T.B., and Wright, C.H.G., "The Signals and Systems Concept Inventory," Proceedings, 2001 ASEE Conference. Paper is through the Signals and Systems Concept Inventory Web Site; contact John Buck or Kathleen Wage for site password.

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